{"id":"https://openalex.org/W2931800015","doi":"https://doi.org/10.1080/11663081.2018.1547513","title":"Monoidal logics: completeness and classical systems","display_name":"Monoidal logics: completeness and classical systems","publication_year":2019,"publication_date":"2019-03-28","ids":{"openalex":"https://openalex.org/W2931800015","doi":"https://doi.org/10.1080/11663081.2018.1547513","mag":"2931800015"},"language":"en","primary_location":{"id":"doi:10.1080/11663081.2018.1547513","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.2018.1547513","pdf_url":null,"source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005406411","display_name":"Clayton Peterson","orcid":"https://orcid.org/0000-0003-0592-2197"},"institutions":[{"id":"https://openalex.org/I292141241","display_name":"Munich School of Philosophy","ror":"https://ror.org/02kqy4228","country_code":"DE","type":"education","lineage":["https://openalex.org/I292141241"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Clayton Peterson","raw_affiliation_strings":["Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I292141241","https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005406411"],"corresponding_institution_ids":["https://openalex.org/I292141241","https://openalex.org/I8204097"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05873082,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"2","first_page":"121","last_page":"151"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monoidal-t-norm-logic","display_name":"Monoidal t-norm logic","score":0.6569243669509888},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6065746545791626},{"id":"https://openalex.org/keywords/t-norm-fuzzy-logics","display_name":"T-norm fuzzy logics","score":0.5995306968688965},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.516158938407898},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.5011098384857178},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.49935388565063477},{"id":"https://openalex.org/keywords/monoidal-category","display_name":"Monoidal category","score":0.45337340235710144},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4507940411567688},{"id":"https://openalex.org/keywords/\u0142ukasiewicz-logic","display_name":"\u0141ukasiewicz logic","score":0.4318810999393463},{"id":"https://openalex.org/keywords/symmetric-monoidal-category","display_name":"Symmetric monoidal category","score":0.4147643446922302},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.39807093143463135},{"id":"https://openalex.org/keywords/substructural-logic","display_name":"Substructural logic","score":0.3568287193775177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3436800241470337},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30723118782043457},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2711288034915924},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.24022361636161804},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16642385721206665},{"id":"https://openalex.org/keywords/many-valued-logic","display_name":"Many-valued logic","score":0.16160133481025696},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.14562326669692993},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.1440306305885315}],"concepts":[{"id":"https://openalex.org/C98224912","wikidata":"https://www.wikidata.org/wiki/Q6901647","display_name":"Monoidal t-norm logic","level":5,"score":0.6569243669509888},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6065746545791626},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.5995306968688965},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.516158938407898},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.5011098384857178},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.49935388565063477},{"id":"https://openalex.org/C2779904274","wikidata":"https://www.wikidata.org/wiki/Q1945014","display_name":"Monoidal category","level":2,"score":0.45337340235710144},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4507940411567688},{"id":"https://openalex.org/C206321295","wikidata":"https://www.wikidata.org/wiki/Q8080919","display_name":"\u0141ukasiewicz logic","level":5,"score":0.4318810999393463},{"id":"https://openalex.org/C98912367","wikidata":"https://www.wikidata.org/wiki/Q17103860","display_name":"Symmetric monoidal category","level":3,"score":0.4147643446922302},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.39807093143463135},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.3568287193775177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3436800241470337},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30723118782043457},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2711288034915924},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24022361636161804},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16642385721206665},{"id":"https://openalex.org/C150889026","wikidata":"https://www.wikidata.org/wiki/Q185502","display_name":"Many-valued logic","level":3,"score":0.16160133481025696},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.14562326669692993},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.1440306305885315},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.0},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.0},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/11663081.2018.1547513","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.2018.1547513","pdf_url":null,"source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2506305459","display_name":null,"funder_award_id":"RO 4548/4-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3148691445","display_name":null,"funder_award_id":"756-2014-0108","funder_id":"https://openalex.org/F4320334617","funder_display_name":"Social Sciences and Humanities Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334617","display_name":"Social Sciences and Humanities Research Council of Canada","ror":"https://ror.org/04j5jqy92"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1968581827","https://openalex.org/W2002130184","https://openalex.org/W2002241150","https://openalex.org/W2018773995","https://openalex.org/W2046363825","https://openalex.org/W2049802486","https://openalex.org/W2054571652","https://openalex.org/W2080908387","https://openalex.org/W2092847864","https://openalex.org/W2093705378","https://openalex.org/W2112970627","https://openalex.org/W2120713972","https://openalex.org/W2130561095","https://openalex.org/W2324455841","https://openalex.org/W2328580899","https://openalex.org/W2495156561","https://openalex.org/W2793576694","https://openalex.org/W2911865844","https://openalex.org/W4210848565","https://openalex.org/W4248156396"],"related_works":["https://openalex.org/W1588682476","https://openalex.org/W169137922","https://openalex.org/W4205339083","https://openalex.org/W4294175725","https://openalex.org/W2310799747","https://openalex.org/W1578365337","https://openalex.org/W1783029874","https://openalex.org/W1529869727","https://openalex.org/W2341378906","https://openalex.org/W1570957963"],"abstract_inverted_index":{"Monoidal":[0],"logics":[1,56,87,126],"were":[2],"introduced":[3],"as":[4],"a":[5,58,139],"foundational":[6],"framework":[7,92],"to":[8,27,33,48,133,144],"analyze":[9],"the":[10,24,70,89,101,145,157,172,182,189],"proof":[11],"theory":[12],"of":[13,60,65,73,93,115,148,159,191],"logical":[14,29,43,61],"systems.":[15,163,196],"Inspired":[16],"by":[17,175],"Lambek's":[18,166],"seminal":[19],"work":[20],"in":[21,31,63,104],"categorical":[22,37,67],"logic,":[23],"objective":[25],"is":[26],"define":[28],"systems":[30,62],"order":[32],"make":[34],"explicit":[35],"their":[36,66,74],"(monoidal)":[38],"structure.":[39],"In":[40,96,153],"this":[41,97],"setting,":[42],"connectives":[44],"can":[45,82],"be":[46,49,83],"proven":[47],"functors":[50],"with":[51,131,142],"specific":[52],"properties.":[53],"Accordingly,":[54],"monoidal":[55,86,110,125],"allow":[57],"classification":[59],"function":[64],"structure":[68],"and":[69,88,111,121,129,150,161,167,180,184,193],"functorial":[71],"properties":[72],"connectives.":[75],"As":[76],"they":[77],"stand,":[78],"however,":[79],"strong":[80],"parallels":[81],"made":[84],"between":[85,109],"broader":[90],"proof-theoretical":[91],"display":[94,135,149],"logics.":[95,113,152],"paper,":[98],"we":[99,122,155,170],"extend":[100],"results":[102],"presented":[103],"Peterson":[105],"((2016).":[106],"A":[107],"comparison":[108],"substructural":[112,151],"Journal":[114],"Applied":[116],"Non-Classical":[117],"Logics,":[118],"26(2),":[119],"126\u2013159)":[120],"show":[123],"that":[124],"are":[127],"sound":[128],"complete":[130],"respect":[132],"associative":[134],"logics,":[136],"thus":[137],"providing":[138],"completeness":[140],"result":[141],"regards":[143],"algebraic":[146],"semantics":[147],"addition,":[154],"discuss":[156,181],"notions":[158],"classical":[160,192],"intuitionistic":[162,194],"Starting":[164],"from":[165],"Grishin's":[168],"analyses,":[169],"explore":[171],"role":[173],"played":[174],"partial":[176],"De":[177],"Morgan":[178],"dualities":[179],"necessary":[183],"sufficient":[185],"conditions":[186],"required":[187],"for":[188],"definitions":[190],"deductive":[195]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
